Future work

One of the issues which I am dealing with in a simplified manner in this paper is output spacing. Lumley 1993 uses the rms of source and receiver inline and crossline spacings. The field data test in this paper is marine, and the synthetics are quasi-marine in their acquisition geometry. For marine geometry it is easy to classify inline aliasing as a second order concern relative to crossline, and essentially ignore it except in the case that energy moves strictly inline. However, the next step in this project is to antialias more difficult land geometries, in particular orthogonal geometries where sources are sparse inline and dense crossline; this will require some more sophisticated answer to the question of spatial sampling.

Also simplified in this project so far is the issue of amplitudes. The amplitude term given by Kirchhoff theory is

$$\frac{\Delta x \Delta y}{2 \pi r_{ij} v} \cos \theta_{ij}$$

where r_ij connects input point i and output point j, and $\theta_{ij}$ is the angle between the normal to the input surface and the traveltime path. This assumes constant sampling and velocity, and infinite aperture, which are in many cases not even approximately realized. In many examples I have found that simpler weights such as $\cos \theta / rv$ or even just unity yield preferable outputs. Intelligent weighting is a future project.